So since draconis is genitive, possible translations could include "The self of the dragon", "The ego of the dragon", "The dragon's self" etc.

I don't think 'ego' is ever used as a noun in Latin; this is modern usage (presumably due to Freud). "The dragon's self", back-translated into Latin, would rather come out as something like "anima draconis". Therefore, I would indeed favor "I of the Dragon" as a translation.

Then again, whoever came up with the title might not have been a Cicero either.